A New Conjugate Gradient Method with Sufficient Descent Property

In this paper, by linearly combining the numerator and denominator terms of the Dai-Liao (DL) and Bamigbola-Ali-Nwaeze (BAN) conjugate gradient methods (CGMs), a general form of DL-BAN method has been proposed. From this general form, a new hybrid CGM, which was found to possess a sufficient descent property is generated. Numerical experiment was carried out on the new CGM in comparison with four existing CGMs, using some set of large scale unconstrained optimization problems. The result showed a superior performance of new method over majority of the existing methods.

A new kind of parameter conjugate gradient for unconstrained optimization

<p>In this paper, a replacement new parameter conjugate gradient for unconstrained optimization. The sufficient descent property cleave to. The global convergence property of the new method is proved under some assumptions. Numerical results explain that the new parameter is superior in practice.<strong></strong></p><p><strong> </strong><em></em></p>

A New Modified Three-Term Hestenes–Stiefel Conjugate Gradient Method with Sufficient Descent Property and Its Global Convergence

This paper describes a modified three-term Hestenes–Stiefel (HS) method. The original HS method is the earliest conjugate gradient method. Although the HS method achieves global convergence using an exact line search, this is not guaranteed in the case of an inexact line search. In addition, the HS method does not usually satisfy the descent property. Our modified three-term conjugate gradient method possesses a sufficient descent property regardless of the type of line search and guarantees global convergence using the inexact Wolfe–Powell line search. The numerical efficiency of the modified three-term HS method is checked using 75 standard test functions. It is known that three-term conjugate gradient methods are numerically more efficient than two-term conjugate gradient methods. Importantly, this paper quantifies how much better the three-term performance is compared with two-term methods. Thus, in the numerical results, we compare our new modification with an efficient two-term conjugate gradient method. We also compare our modification with a state-of-the-art three-term HS method. Finally, we conclude that our proposed modification is globally convergent and numerically efficient.